\(\begin{aligned} {\text{Prevalence}} = \frac{\text{TP + FN}}{\text{TP + FP + TN + FN}} \end{aligned}\)
\(\begin{aligned} {\text{PPCR (Predicted Positives Condition Rate)}} = \frac{\text{TP + FP}}{\text{TP + FP + TN + FN}} \end{aligned}\)
\(\begin{aligned} \text{Sensitivity (Recall, True Positive Rate)} = \frac{\text{TP}}{\text{TP + FN}} = \frac{\text{TP}}{\text{Real Positives}} = \text{Prob( Predicted Positive | Real Positive )} \end{aligned}\)
\(\begin{aligned} \text{Specificity (True Negative Rate)} = \frac{\text{TN}}{\text{TN + FP}} = \frac{\text{TN}}{\text{Real Negatives}} = \text{Prob( Predicted Negative | Real Negative )} \end{aligned}\)
\(\begin{aligned} \text{PPV (Precision)} = \frac{\text{TP}}{\text{TP + FP}} = \frac{\text{TP}}{\text{Predicted Positives}} = \text{Prob( Real Positive | Predicted Positive )} \end{aligned}\)
\(\begin{aligned} \text{NPV} = \frac{\text{TN}}{\text{TN + FN}} = \frac{\text{TN}}{\text{Predicted Negatives}} = \text{Prob( Real Negative | Predicted Negative )} \end{aligned}\)
\(\begin{aligned} \text{Lift} = \frac{\text{PPV}}{\text{Prevalence}} = \frac{\cfrac{\text{TP}}{\text{TP + FP}}}{\cfrac{\text{TP + FN}}{\text{TP + FP + TN + FN}}} \end{aligned}\)
\(\begin{aligned} \text{Net Benefit} = \frac{\text{TP}}{\text{TP + FP + TN + FN}} - \frac{\text{FP}}{\text{TP + FP + TN + FN}} * {\frac{{p_{t}}}{{1 - p_{t}}}} \end{aligned}\)
## # A tibble: 10 x 4
## model quintile phaty phatx
## <fct> <int> <dbl> <dbl>
## 1 model 1 1 0 0.0000178
## 2 model 1 2 0.000626 0.000104
## 3 model 1 3 0.00125 0.000330
## 4 model 1 4 0.000626 0.000849
## 5 model 1 5 0.00188 0.00202
## 6 model 1 6 0.00501 0.00462
## 7 model 1 7 0.00939 0.0108
## 8 model 1 8 0.0157 0.0270
## 9 model 1 9 0.0307 0.0841
## 10 model 1 10 0.470 0.455
## [1] -0.02348153 0.49311209## # A tibble: 10 x 4
## model quintile phaty phatx
## <fct> <int> <dbl> <dbl>
## 1 model 1 1 0 0.0000178
## 2 model 1 2 0.000626 0.000104
## 3 model 1 3 0.00125 0.000330
## 4 model 1 4 0.000626 0.000849
## 5 model 1 5 0.00188 0.00202
## 6 model 1 6 0.00501 0.00462
## 7 model 1 7 0.00939 0.0108
## 8 model 1 8 0.0157 0.0270
## 9 model 1 9 0.0307 0.0841
## 10 model 1 10 0.470 0.455
## [1] -0.02348153 0.49311209